Error

Derivation

1. Initial program 18.4

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\]
2. Using strategy rm

3. Applied times-frac1.2

   \[\leadsto \color{blue}{\frac{-t1}{t1 + u} \cdot \frac{v}{t1 + u}}\]
4. Using strategy rm

5. Applied add-cube-cbrt2.0

   \[\leadsto \frac{-t1}{\color{blue}{\left(\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}\right) \cdot \sqrt[3]{t1 + u}}} \cdot \frac{v}{t1 + u}\]

6. Applied add-cube-cbrt1.5

   \[\leadsto \frac{-\color{blue}{\left(\sqrt[3]{t1} \cdot \sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}}}{\left(\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}\right) \cdot \sqrt[3]{t1 + u}} \cdot \frac{v}{t1 + u}\]

7. Applied distribute-rgt-neg-in1.5

   \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{t1} \cdot \sqrt[3]{t1}\right) \cdot \left(-\sqrt[3]{t1}\right)}}{\left(\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}\right) \cdot \sqrt[3]{t1 + u}} \cdot \frac{v}{t1 + u}\]

8. Applied times-frac1.5

   \[\leadsto \color{blue}{\left(\frac{\sqrt[3]{t1} \cdot \sqrt[3]{t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \frac{-\sqrt[3]{t1}}{\sqrt[3]{t1 + u}}\right)} \cdot \frac{v}{t1 + u}\]

9. Applied associate-*l*1.1

   \[\leadsto \color{blue}{\frac{\sqrt[3]{t1} \cdot \sqrt[3]{t1}}{\sqrt[3]{t1 + u} \cdot \sqrt[3]{t1 + u}} \cdot \left(\frac{-\sqrt[3]{t1}}{\sqrt[3]{t1 + u}} \cdot \frac{v}{t1 + u}\right)}\]

10. Final simplification1.1

    \[\leadsto \frac{\left(-\sqrt[3]{t1}\right) \cdot \sqrt[3]{t1}}{\sqrt[3]{u + t1} \cdot \sqrt[3]{u + t1}} \cdot \left(\frac{\sqrt[3]{t1}}{\sqrt[3]{u + t1}} \cdot \frac{v}{u + t1}\right)\]

Reproduce

herbie shell --seed 2019100 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))